No abstract available

[en] In this paper we quantize the massive abelian p-form gauge fields in D dimensions in the context of the Hamiltonian BRST formalism. Extending the original phase-space in order to reveal the reducibility of a certain first-class system, we obtain that quantizing the original theory is the same as quantizing a (p-1)-order reducible system using BRST. This system describes abelian p-form gauge fields interacting through a current-current term with abelian (p-1)-form gauge fields. For p=1 and D=4 we recover the Stueckelberg coupling. (author)

[en] The volume operator plays a pivotal role for the quantum dynamics of loop quantum gravity (LQG). It is essential to construct triad operators that enter the Hamiltonian constraint and which become densely defined operators on the full Hilbert space, even though in the classical theory the triad becomes singular when classical GR breaks down. The expression for the volume and triad operators derives from the quantization of the fundamental electric flux operator of LQG by a complicated regularization procedure. In fact, there are two inequivalent volume operators available in the literature and, moreover, both operators are unique only up to a finite, multiplicative constant which should be viewed as a regularization ambiguity. Now on the one hand, classical volumes and triads can be expressed directly in terms of fluxes and this fact was used to construct the corresponding volume and triad operators. On the other hand, fluxes can be expressed in terms of triads and triads can be replaced by Poisson brackets between the holonomy and the volume operators. Therefore one can also view the holonomy operators and the volume operator as fundamental and consider the flux operator as a derived operator. In this paper we mathematically implement this second point of view and thus can examine whether the volume, triad and flux quantizations are consistent with each other. The results of this consistency analysis are rather surprising. Among other findings we show the following. (1) The regularization constant can be uniquely fixed. (2) One of the volume operators can be ruled out as inconsistent. (3) Factor ordering ambiguities in the definition of triad operators are immaterial for the classical limit of the derived flux operator. The results of this paper show that within full LQG triad operators are consistently quantized. In this paper we merely present ideas and the results of the consistency check. In a companion paper we supply detailed proofs

[en] We discuss the general structure of relativistic theories in 2+1 dimensions which physical states carry fractional spin and statistics at both the first-quantized and second-quantized level. We show that the Poincare representations carried by the physical states of the theory are modified by coupling the particle-number current to a topological term. We discuss the spin-statistics theorem and the dependence of the total angular momentum on the number of particles and we show that due to short-distance divergencies they are different in the first- and second-quantized theories. (author)

[en] The quantum analogue of an area preserving map on a compact phase space is a unitary (evolution) operator which can be represented by a matrix of dimension L∝ℎ_-1. The semiclassical theory for spectrum of the evolution operator will be reviewed with special emphasize on developing a dynamical zeta function approach, similar to the one introduced recently for a semiclassical quantization of hamiltonian systems. (author)

[en] A quantum-mechanical system of N spin-1/2 identical particles, where γ matrices anticommute for different particles, is shown to escape the procedure of the second quantization (in the physical space). Instead, a quantization procedure in the Fock configurational space, called here the third quantization, is outlined. The respective particles are reffered to as the non-Abelian Dirac particles. A system of N such particles, tightly concentrated around its centre of mass, can always be described in the pointlike limit by the Dirac equation corresponding to a composite, reducible (for N > 1) representation of the Dirac algebra. According to a previous author's discussion such representations with N = 1,3,5 may be responsible for the puzzling phenomenon of three fermion generations, if an intrinsic exclusion principle is introduced. (author)

[en] We consider the commutative limit of matrix geometry described by a large-N sequence of some Hermitian matrices. Under some assumptions, we show that the commutative geometry possesses a Kähler structure. We find an explicit relation between the Kähler structure and the matrix configurations which define the matrix geometry. We also discuss a relation between the matrix configurations and those obtained from the geometric quantization.

[en] The modified action of Siegel for a point superparticle is quantized by using the BRS transformation. The second quantization is also discussed. (author)

[en] We study numerically classical and quantum dynamics of a piecewise parabolic area preserving map on a cylinder which emerges from the bounce map of elongated triangular billiards. The classical map exhibits anomalous diffusion. Quantization of the same map results in a system with dynamical localization and pure point spectrum

[en] We generalize the Lieb-Robinson theorem to systems whose Hamiltonian is the sum of local operators whose commutators are bounded.